# 5 sets of 5 options, how many possible combinations?

Apologies in advance if this was already answered somewhere, I tried searching but didn't really know what to search for which is the same issue I'm having with Google. I really appreciate your help with this!!

I need to figure out how many combinations are possible of the following sets. I think that I just multiply everything together can anyone confirm that for me?

Example 1: 5 sets of 5 options. So there's (a1, a2, a3, a4, and a5) in one set, (b1, b2, b3, b4, and b5) in the next and there's c, d, and e all with 5 in the set. To figure out all the possible combinations would that just be 5*5*5*5*5= 3125?

Do I have that right?

• If you are selecting one element from each set, your answer is correct. – N. F. Taussig Jan 5 at 10:49

If you need exactly one element of each set, and in the specific order of $$\\$$ a -> b -> c -> d -> e, $$\\$$ then yes. If not, it depends on how you pick the elements to make the new randomized set.
• Yes. In this case you can even form a 5-dimensional grid, with ordered dimensions. Each cell in the grid represents a possible arrangement, are all distincts and all the possible arrangements are listed in the grid, so take $5^5$ and it does it. – charlesleninja Jan 7 at 21:19